The present invention relates to an involute interpolation speed control system to be used in machining by numerical control apparatuses and the like, and more specifically, to an involute interpolation speed control system for controlling a commanded speed in an involute interpolation to which a cutter compensation is applied.
There is a great need for the interpolation of involute curves in numerical control apparatuses or the like, when machining gears, pump impellers, or the like, and it is general practice to interpolate an involute curve with a computer or an NC programming device separate from a numerical control apparatus, convert the interpolated data to linear data on a tape, and machine a workpiece under a numerical control using the tape.
The applicant filed an application for an involute interpolation speed control system by which an involute curve is simply interpolated in a numerical control apparatus, and the speed in tangential direction thereof is made constant regardless of an angular speed, as Japanese Patent Application No. 62-157302 (Japanese Patent Laid-Open Publication No. 64-2106).
In the involute interpolation speed control system, the coordinate of a point on an involute curve is defined by the following equations. EQU X.sub.n =R{cos(.theta..sub.n +.theta..sub.0)+.theta..sub.n sin(.theta..sub.n +.theta..sub.0)}+X.sub.o EQU Y.sub.n =R{sin(.theta..sub.n +.theta..sub.0)-.theta..sub.n cos(.theta..sub.n +.theta..sub.0)}+Y.sub.o
.theta..sub.n is incremented by an amount determined by the following equation in the range of from .theta..sub.n =(.theta..sub.s -.theta..sub.0) to .theta..sub.n =(.theta..sub.e -.theta..sub.0), where s is a starting point and e is an end point. EQU .theta..sub.n+1 =.theta..sub.n +K/(R.multidot..theta..sub.n)
Then, a point X.sub.n+1, Y.sub.n+1 corresponding thereto is determined from the above equations, and a difference between the previous point and the present point is determined, whereby the involute curve is interpolated. The interpolation is carried out in such a manner that the increment of .theta..sub.n is set to a value, K/(R.multidot..theta..sub.n) which is inversely proportional to the increase in the angle so that the speed in the tangential direction is kept at a constant value.
The conventional involute interpolation speed control system is such that, when a cutter is compensated, an involute curve is interpolated to enable a speed in a tangential direction of the cutter on the path through which the center thereof moves (cutter path) to coincide at all times with a commanded feed speed. Therefore, as shown in FIG. 4, a cutter W is offset to the concave side of an involute curve (path commanded by a program) In1, and a ratio of a speed in a tangential direction of the cutter W at the center thereof to a cutting speed at an actual cutting point Pss is made equal to a ratio of a value obtained by subtracting a cutter radius from the radius of curvature of an involute curve (cutter path) In2 at the cutting point Pss to the above radius of curvature. This ratio is made larger as the cutter W approaches a basic circle C and as a result, an actual cutting speed is made larger than a commanded feed speed. Whereas, when the cutter W is offset to the convex side of the involute curve In1, as the cutter W approaches the basic circle C, the actual cutting speed is made smaller than the commanded feed speed.
Therefore, a problem arises in that a speed of the outer circumference (cutting point Pss) of the cutter on the path In2 commanded by the program, which is the actual cutting speed, is constantly changed in accordance with the change of curvature of the involute curve, and thus a workpiece cannot be smoothly machined.